Question

How do you verify? `(cos2x)/ (1+sin2x) =(1-tanx)/(1+tanx)`

Answer 1

`LHS=(cos2x)/ (1+sin2x)`

`=(cos^2x-sin^2x)/ (cos^2x +sin^2x+2cosxsinx)`

`=(cos^2x-sin^2x)/ (cosx +sinx)^2`

`=(cosx-sinx)/ (cosx +sinx)`

`=(cosx/cosx-sinx/cosx)/ (cosx/cosx +sinx/cosx)`

`=(1-tanx)/(1+tanx)=RHS`